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Mathematics
Mathematics
Problem
If
m
,
n
∈
N
m, n \in N
m
,
n
∈
N
, then the value of
∫
a
b
(
x
−
a
)
m
(
b
−
x
)
n
d
x
\int_{a}^{b} (x-a)^m (b-x)^n dx
∫
a
b
(
x
−
a
)
m
(
b
−
x
)
n
d
x
is equal to a.
(
b
−
a
)
m
+
n
⋅
m
!
n
!
(
m
+
n
)
!
\frac{(b-a)^{m+n} \cdot m! n!}{(m+n)!}
(
m
+
n
)!
(
b
−
a
)
m
+
n
⋅
m
!
n
!
b.
(
b
−
a
)
m
+
n
+
1
⋅
m
!
n
!
(
m
+
n
+
1
)
!
\frac{(b-a)^{m+n+1} \cdot m! n!}{(m+n+1)!}
(
m
+
n
+
1
)!
(
b
−
a
)
m
+
n
+
1
⋅
m
!
n
!
c.
(
b
−
a
)
m
⋅
m
!
m
!
\frac{(b-a)^m \cdot m!}{m!}
m
!
(
b
−
a
)
m
⋅
m
!
d. None of these
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